1. Field of the Invention
The present invention relates to force balancing of a Coriolis flow meter.
2. Statement of the Problem
Vibrating conduit sensors, such as Coriolis mass flow meters, typically operate by detecting motion of a vibrating conduit that contains a material. Properties associated with the material in the conduit, such as mass flow, density and the like, in the conduit may be determined by processing signals from motion transducers associated with the conduit, as the vibration modes of the vibrating material-filled system generally are affected by the combined mass, stiffness and damping characteristics of the containing conduit and the material contained therein.
A typical Coriolis mass flow meter includes one or more conduits that are connected inline in a pipeline or other transport system and convey material, e.g., fluids, slurries and the like, in the system. Each conduit may be viewed as having a set of natural vibration modes including, for example, simple bending, torsional, radial and coupled modes. In a typical Coriolis mass flow measurement application, a conduit is excited in one or more vibration modes as a material flows through the conduit, and motion of the conduit is measured at points spaced along the conduit. Excitation is typically provided by an actuator, e.g., an electromechanical device, such as a voice coil-type driver, that perturbs the conduit in a periodic fashion. Mass flow rate may be determined by measuring time delay or phase differences between motion at the transducer locations.
The magnitude of the time delay is very small; often measured in nanoseconds. Therefore, it is necessary to have the transducer output be very accurate. Transducer accuracy may be compromised by nonlinearities and asymmetries in the meter structure or from motion arising from extraneous forces. For example, A Coriolis mass flow meter having unbalanced components can vibrate its case, flanges and the pipeline at the drive frequency of the meter. This vibration perturbs the time delay signal in an amount that depends on the rigidity of the mount. Since the rigidity of the mount is generally unknown and can change over time and temperature, the effects of the unbalanced components cannot be compensated and may significantly affect meter performance. The effects of these unbalanced vibrations and mounting variations are reduced by using flow meter designs that are balanced and by using signal processing techniques to compensate for unwanted components of motion.
The balanced vibration discussed above involves only a single direction of vibration: the Z-direction. The Z-direction is the direction that the conduits are displaced as they vibrate. Other directions, including the X-direction along the pipeline and the Y-direction perpendicular to the Z and X-directions, are not balanced. This reference coordinate system is important because Coriolis flow meters produce a secondary sinusoidal force in the Y-direction. This force creates a meter vibration in the Y-direction that is not balanced, resulting in meter error.
One source of this secondary force is the location of the mass of the meter driver assembly. A typical driver assembly consists of a magnet fastened to one conduit and a coil of conductive wire fastened to another conduit. The Y-vibration is caused by the center of mass of the driver magnet and the center of mass of the driver coil not lying on the respective X-Y planes of the centerline(s) of the flow conduit(s). The X-Y planes are necessarily spaced apart to keep the conduits from interfering with one another. The centers of mass of the magnet and/or coil are offset from their planes because the coil needs to be concentric with the end of magnet to be at the optimum position in the magnetic field.
A flow conduit, when driven to vibrate, does not truly translate but rather cyclically bends about the locations at which it is fixed. This bending can be approximated by rotation about the fixed point(s). The vibration is then seen to be a cyclic rotation through a small angle about its center of rotation, CR. The angular vibration amplitude is determined from the desired vibration amplitude in the Z direction and the distance, d, from the center of rotation of the conduit center at the driver location. The angular amplitude of vibration, Δθ, is determined from the following relation:Δθ=arctan (ΔZ/d)  (1)
The offset of the driver component (magnet or coil assembly) center of mass from the conduit centerline causes the driver component center of mass to have a Y-component of its vibration. The driver component mass usually has an offset in the Z-direction that is at least equal to the conduit radius. The angular offset, Φ, from the conduit centerline is thus not negligible. The driver component mass oscillates about its offset position with the same angular amplitude as the flow conduit, Δθ. Approximating the motion of the driver mass as being perpendicular to the line connecting the driver center of mass with the center of rotation, CR, the driver mass Y-direction motion, ΔYm, can be solved from the following:ΔYm=ΔZ sin (φ)   (2)
The Y-direction motion of the driver component mass causes the whole meter to vibrate in the Y-direction. Conservation of momentum requires that, for a freely suspended meter, the Y-direction vibration of the entire meter is equal to the Y-direction vibration amplitude of the driver mass times the ratio of the driver mass divided by the meter mass. This Y-vibration of the entire meter is a direct result of the desired conduit vibration in Z in conjunction with the angular offset of the drive components' centers of mass. This coupling between the desired conduit vibration and the undesired Y-vibration of the entire meter means that damping of the meter Y-vibration damps the flow conduit vibration in Z, and that a stiff meter mount raises conduit frequency while a soft meter mount lowers conduit frequency. The change in conduit frequency with mounting stiffness has been observed experimentally in meters with high Y-vibration amplitude. It is a problem because conduit frequency is used to determine fluid density and frequency is also an indication of conduit stiffness. Changes in conduit stiffness due to mounting stiffness change the calibration factor of the meter. The direct coupling between the drive vibration and the local environment also results in an unstable zero (a flow signal when no flow is present) of the meter.